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United States Patent 
6,069,977

Kim
, et al.

May 30, 2000

Image compression method using wavelet transform techniques
Abstract
An image compression method is provided which uses a wavelet transform
technique to generate transform coefficients relating to an input image.
Furthermore, the method generates and encodes an efficient tree structure
of the transform coefficients by performing the following steps. First,
transform coefficients are obtained by transforming an input image in
accordance with the wavelet transforming technique. Then, a quantizing
interval which minimizes quantization errors is determined for a
predetermined step size and is determined according to statistical
characteristics of the input image. Then, a simple tree structure is
generated based on the transform coefficients, and such tree structure is
modified by using statistical characteristics of the transform
coefficients to produce a monotonically decreasing tree structure. The
resultant tree structure is modified by limiting a maximum height
difference between parent nodes and child nodes of the tree structure to
produce the tree list. In addition, the transform coefficients may be
quantized based on the quantizing interval to produce quantized transform
coefficients, and the modified tree list and the quantized transform
coefficients may be arithmeticlly coded.
Inventors:

Kim; Yougkyu (Kwacheon, KR);
Park; Kyutae (Seoul, KR);
Lee; Imgeun (Seoul, KR);
Kim; Jongsik (Seoul, KR)

Assignee:

Samsung Electronics Co., Ltd. (KyungkiDo, KR)

Appl. No.:

588895 
Filed:

January 19, 1996 
Foreign Application Priority Data
Current U.S. Class: 
382/240; 375/240.03; 382/248 
Intern'l Class: 
G06K 009/36; H04N 007/12 
Field of Search: 
348/398,390,384,405,415
382/240,248,168,169,232

References Cited
U.S. Patent Documents
5321776  Jun., 1994  Shapiro  382/240.

Other References
Kim et al, "New tree structure with conditional height difference for
wavelet transform image coding" Electronics Letters Jan. 1995 vol. 31, No.
2.

Primary Examiner: Lee; Thomas D.
Assistant Examiner: Chen; Wenpeng
Attorney, Agent or Firm: Sughrue, Mion, Zinn, Macpeak & Seas, PLLC
Claims
What is claimed is:
1. An image compression method which uses a wavelet transform technique and
which converts an input image into coded data of an output compressed
image, comprising the steps of:
(a) inputting said input image and obtaining transform coefficients by
transforming said input image in accordance with said wavelet transforming
technique;
(b) determining a quantizing interval which minimizes quantization errors
in a predetermined step size, wherein said quantizing interval is
determined according to statistical characteristics of said input image;
(c) generating a simple tree structure based on said transform
coefficients;
(d) modifying said simple tree structure by using statistical
characteristics of said transform coefficients to produce a monotonically
decreasing tree structure, wherein said monotonically decreasing tree
structure comprises a parent node and child nodes which correspond to said
parent node;
(e) modifying said monotonically decreasing tree structure by limiting a
maximum height difference between said parent node and said child nodes to
produce a modified tree list;
(f) quantizing said transform coefficients based on said quantizing
interval to produce quantized transform coefficients; and
(g) arithmetically coding said modified tree list and said quantized
transform coefficients to produce said coded data, wherein said coded data
corresponds to said output compressed image.
2. An image compression method according to claim 1, wherein said step (b)
of determining said quantizing interval comprises the steps of:
(b1) obtaining a density function p(x) based on a histogram of said
transform coefficients, wherein said density function p(x) is a function
of x and wherein x corresponds to data relating to said input image;
(b2) manipulating said density function p(x) such that said density
function approximates a piece wise linear function; and
(b3) determining said quantizing interval having minimal quantization
errors based on said piece wise liner function.
3. An image compression method according to claim 2, wherein said
quantizing interval satisfies the equation:
##EQU14##
wherein said density function p(x) equals ax+b, a and b are arbitrary
constants, k is an integer, G is said predetermined step size, r is a
constant determined by said statistical characteristics of said input
image and said predetermined step size G, and kG is a quantization value,
and
wherein said quantizing interval is defined by [kGr, (k+1)Gr)].
4. An image compression method according to claim 1, wherein said step (c)
of generating said simple tree structure comprises the step of:
(c1) determining a height h(C.sub.ij) of said transform coefficients
C.sub.ij,
wherein said height h(C.sub.ij) satisfies the equation:
##EQU15##
wherein said height h(C.sub.ij) equals zero if .vertline.C.sub.ij
.vertline.<Gr and .Ebackward.m .epsilon. Dc.sub.ij for
.vertline.m.vertline..ltoreq.G,
wherein said height h(C.sub.ij) equals NULL if .vertline.C.sub.ij
.vertline.<Gr and .Ainverted.m .epsilon. Dc.sub.ij for
.vertline.m.vertline.<G, wherein said height h(C.sub.ij) is deemed not to
exist if said height h(C.sub.ij) equals NULL, and
wherein Dc.sub.ij represents sets of values of said child nodes
respectively corresponding to said transform coefficients C.sub.ij, G
equals said predetermined step size, r is a constant determined by said
statistical characteristics of said input image and said predetermined
step size G, i equals a first set of integers, j equals a second set of
integers, and m is an element of said sets of values of said child nodes.
5. An image compression method according to claim 4, wherein said step (d)
of modifying said simple tree structure to produce said monotonically
decreasing tree structure comprises the step of:
(d1) modifying tree information T(i,j) which corresponds to said transform
coefficient C.sub.ij and which is contained in said simple tree structure,
wherein said tree information T(i,j) is modified in accordance with the
following equation:
##EQU16##
6. An image compression method according to claim 5, wherein said step (e)
of modifying said monotonically decreasing tree structure to produce said
modified tree list comprises the steps of: (e1) limiting a height
difference Diff(C.sub.ij) between said parent node and said child nodes in
accordance with the equations:
T(i,j)=T(i.sub.p,j.sub.p)Maxdiff if T(i.sub.p,j.sub.p)T(i,j)>Maxdiff,
and
T(i,j)=T(i.sub.p,j.sub.p)Diff(C.sub.ij) if
T(i.sub.p,j.sub.p)T(i,j).ltoreq.Maxdiff,
wherein T(i.sub.p,j.sub.p) equals tree information which corresponds to one
of said transform coefficients C.sub.ij that relates to said parent node,
T(i,j) equals tree information which corresponds to said transform
coefficients C.sub.ij that relate to said child nodes, and Maxdiff is said
maximum height difference between said parent node and said child nodes.
7. An image compression method according to claim 1, wherein said step (g)
of arithmetically coding said modified tree list comprises the steps of:
(g1) separating a set S of symbols in said modified tree list into N
subsets S.sub.1 to S.sub.N, wherein said symbols relate to said input
image and wherein said subsets S.sub.1 to S.sub.N are capable of being
independently coded and decoded;
(g2) determining a particular subset S.sub.i of said subsets S.sub.1 to
S.sub.N to which particular symbols of said symbols belong based on
previously coded information contained within said modified tree list;
(g3) coding said particular symbols which correspond to said particular
subset S.sub.i by an arithmetic coder which corresponds to said particular
subset S.sub.i ; and
(g4) arithmetically coding at least one of said quantized transform
coefficients by dividing said at least one of said quantized transform
coefficients into code data and size data and arithmetically coding said
code data and said size data.
8. A method of generating quantized data based on transform coefficients
corresponding to an input image, wherein said method comprises the steps
of:
(a) inputting said input image;
(b) obtaining said transform coefficients by transforming said input image
in accordance with a wavelet transform technique;
(c) obtaining a density function p(x) based on a histogram of said
transform coefficients;
(d) manipulating said density function p(x) such that said density function
approximates a piece wise linear function;
(e) determining a quantizing interval having minimal quantization errors
for a predetermined step size based on said piece wise liner function; and
(f) quantizing said transform coefficients based on said quantizing
interval to produce said quantized data corresponding to said input image.
9. A method of quantization according to claim 8, wherein said quantizing
interval satisfies the equation:
##EQU17##
wherein said density function p(x) equals ax+b, a and b are arbitrary
constants, k is a real number, G is said predetermined step size, r is a
positive number, and kG is a quantization value, and
wherein said quantizing interval is defined by [kGr, (k+1)Gr)].
10. A method of generating a tree list based on transform coefficients
corresponding to an input image, comprising the steps of:
(a) inputting said input image;
(b) obtaining said transform coefficients by transforming said input image
in accordance with a wavelet transform technique;
(c) generating a simple tree structure which corresponds to said transform
coefficients by determining a height h(C.sub.ij) for each of at least some
of said transform coefficients C.sub.ij,
wherein said height h(C.sub.ij) satisfies the equation:
##EQU18##
wherein said height h(C.sub.ij) equals zero if .vertline.C.sub.ij
.vertline.<Gr and .Ebackward.m .epsilon. Dc.sub.ij for
.vertline.m.vertline..gtoreq.G,
wherein said height h(C.sub.ij) equals NULL if .vertline.C.sub.ij
.vertline.<Gr and .Ainverted.m .epsilon. Dc.sub.ij for
.vertline.m.vertline.<G wherein said height h(C.sub.ij) is deemed not to
exist if said height h(C.sub.ij) equals NULL, and
wherein Dc.sub.ij represents sets of values of child nodes within said
simple tree structure, said child nodes respectively correspond to said
transform coefficients C.sub.ij, G equals a predetermined step size, r is
a positive number, i equals a first set of integers, j equals a second set
of integers, and m is an element of said sets of values of said child
nodes; and
(d) generating simple tree structure data corresponding to said simple tree
structure.
11. A method of generating a tree list according to claim 10, further
comprising the step of:
(e) modifying said simple tree structure to produce a monotonically
decreasing tree structure by modifying tree information T(i,j) which
corresponds to said transform coefficients C.sub.ij and which is contained
in said simple tree structure, wherein said tree information T(i,j) is
modified in accordance with the following equation:
##EQU19##
12. A method of generating a tree list according to claim 11, further
comprising the step of: (f) modifying said monotonically decreasing tree
structure to produce said tree list by:
(f1) limiting a height difference Diff(C.sub.ij) between a parent node and
said child nodes in accordance with the equations:
T(i,j)=T(i.sub.p,j.sub.p)Maxdiff if T(i.sub.p,j.sub.p)T(i,j)>Maxdiff,
and
T(i,j)=T(i.sub.p,j.sub.p)Diff(C.sub.ij) if
T(i.sub.p,j.sub.p)T(i,j).ltoreq.Maxdiff,
wherein T(i.sub.p,j.sub.p) equals tree information which corresponds to one
of said transform coefficients C.sub.ij that relates to said parent node,
T(i,j) equals tree information which corresponds to said transform
coefficients C(.sub.ij) that relate to said child nodes, and Maxdiff is a
predetermined maximum height difference between said parent node and said
child nodes,
wherein said tree list corresponds to said input image.
13. A method of coding a tree list corresponding to an input image, wherein
said method comprises the steps of:
(a) inputting said input image;
(b) transforming said input image into transform coefficients based on a
wavelet transform technique;
(c) generating said tree list based on said transform coefficients;
(d) separating a set S of symbols in said tree list into N subsets S.sub.1
to S.sub.N, wherein said symbols relate to said input image and wherein
said subsets S.sub.1 to S.sub.N are capable of being independently coded
and decoded;
(e) determining a first particular subset S.sub.i of said subsets S.sub.1
to S.sub.N to which first particular symbols of said symbols belong based
on previously coded information which is contained within said tree list;
and
(f) coding said first particular symbols which correspond to said first
particular subset S.sub.i by a first arithmetic coder which corresponds to
said first particular subset S.sub.i, wherein said first arthimetic coder
codes said first particular symbols into first coded symbol data that
corresponds to said input image;
(g) determining a second particular subset S.sub.j of said subsets S.sub.1
to S.sub.N to which second particular symbols of said symbols belong based
on previously coded information which is contained within said tree list;
and
(h) coding said second particular symbols which correspond to said second
particular subset S.sub.j by a second arithmetic coder which corresponds
to said second particular subset S.sub.j, wherein said second arthimetic
coder codes said second particular symbols into second coded symbol data
that corresponds to said input image.
14. A method of coding a tree list according to claim 13, wherein said
method further comprises the step of:
(i) arithmetically coding a quantized transform coefficient by dividing
said quantized transform coefficient into code data and size data and
arithmetically coding said code data and said size data, wherein said
quantized transform coefficient corresponds to at least one of said
transform coefficients.
15. An image compression method which uses a wavelet transform technique
and which converts an input image into an output compressed image,
comprising the steps of:
(a) inputting said input image and obtaining transform coefficients by
transforming said input image in accordance with said wavelet transforming
technique;
(b) determining a quantizing interval which minimizes quantization errors
in a predetermined step size, wherein said quantizing interval is
determined according to statistical characteristics of said input image;
(c) generating a simple tree structure based on said transform
coefficients;
(d) modifying said simple tree structure by using statistical
characteristics of said transform coefficients to produce a monotonically
decreasing tree structure, wherein said monotonically decreasing tree
structure comprises a parent node and child nodes which correspond to said
parent node; and
(e) modifying said monotonically decreasing tree structure by limiting a
maximum height difference between said parent node and said child nodes to
produce a modified tree list and generating modified tree list data which
corresponds to said output compressed image.
16. An image compression method according to claim 15, wherein said step
(b) of determining said quantizing interval comprises the steps of:
(b1) obtaining a density function p(x) based on a histogram of said
transform coefficients, wherein said density function p(x) is a function
of x and wherein x corresponds to data relating to said input image;
(b2) manipulating said density function p(x) such that said density
function approximates a piece wise linear function; and
(b3) determining said quantizing interval having minimal quantization
errors based on said piece wise liner function.
17. An image compression method according to claim 16, wherein said
quantizing interval satisfies the equation:
##EQU20##
wherein said density function p(x) equals ax+b, a and b are arbitrary
constants, k is an integer, G is said predetermined step size, r is a
constant determined by said statistical characteristics of said input
image and said predetermined step size G, and kG is a quantization value,
and
wherein said quantizing interval is defined by [kGr, (k+1)Gr)].
18. An image compression method according to claim 15, wherein said step
(c) of generating said simple tree structure comprises the step of:
(c1) determining a height h(C.sub.ij) of said transform coefficients
C.sub.ij,
wherein said height h(C.sub.ij) satisfies the equation:
##EQU21##
wherein said height h(C.sub.ij) equals zero if .vertline.C.sub.ij
.vertline.<Gr and .Ebackward.m .epsilon. Dc.sub.ij for
.vertline.m.vertline..gtoreq.G,
wherein said height h(C.sub.ij) equals NULL if .vertline.C.sub.ij
.vertline.<Gr and .Ainverted.m .epsilon. Dc.sub.ij for
.vertline.m.vertline.<G, wherein said height h(C.sub.ij) is deemed not to
exist if said height h(C.sub.ij) equals NULL, and
wherein Dc.sub.ij represents sets of values of said child nodes
respectively corresponding to said transform coefficients C.sub.ij, G
equals said predetermined step size, r is a constant determined by said
statistical characteristics of said input image and said predetermined
step size G, i equals a first set of integers, j equals a second set of
integers, and m is an element of said sets of values of said child nodes.
19. An image compression method according to claim 18, wherein said step
(d) of modifying said simple tree structure to produce said monotonically
decreasing tree structure comprises the step of:
(d1) modifying tree information T(i,j) which corresponds to said transform
coefficient C.sub.ij and which is contained in said simple tree structure,
wherein said tree information T(i,j) is modified in accordance with the
following equation:
##EQU22##
20.
20. An image compression method according to claim 19, wherein said step
(e) of modifying said monotonically decreasing tree structure to produce
said modified tree list comprises the steps of: (e1) limiting a height
difference Diff(C.sub.ij) between said parent node and said child nodes in
accordance with the equations:
T(i,j)=T(i.sub.p,j.sub.p)Maxdiff if T(i.sub.p,j.sub.p)T(i,j)>Maxdiff,
and
T(i,j)=T(i.sub.p,j.sub.p)Diff(C.sub.ij) if
T(i.sub.p,j.sub.p)T(i,j).ltoreq.Maxdiff,
wherein T(i.sub.p,j.sub.p) equals tree information which corresponds to one
of said transform coefficients C.sub.ij that relates to said parent node,
T(i,j) equals tree information which corresponds to said transform
coefficients C.sub.ij that relate to said child nodes, and Maxdiff is said
maximum height difference between said parent node and said child nodes.
21. A method of generating quantized interval data based on transform
coefficients corresponding to an input image, wherein said method
comprises the steps of:
(a) inputting said input image;
(b) obtaining said transform coefficients by transforming said input image
in accordance with a wavelet transform technique;
(c) obtaining a density function p(x) based on a histogram of said
transform coefficients;
(d) manipulating said density function p(x) such that said density function
approximates a piece wise linear function; and
(e) determining a quantizing interval having minimal quantization errors
for a predetermined step size based on said piece wise liner function to
produce said quantized interval data corresponding to said input image.
22. A method of quantization according to claim 21, wherein said quantizing
interval satisfies the equation:
##EQU23##
wherein said density function p(x) equals ax+b, a and b are arbitrary
constants, k is a real number, G is said predetermined step size, r is a
positive number, and kG is a quantization value, and
wherein said quantizing interval is defined by [kGr, (k+1)Gr)].
Description
FIELD OF THE INVENTION
The present invention relates to a compression coding method which uses a
wavelet transform (WT) technique. More particularly, the invention
pertains to a quantization method in which a quantization error is reduced
and pertains to a method for creating an effective tree list for coding a
compressed image. Furthermore, this application corresponds to Korean
Patent Application No. 9513684.
BACKGROUND OF THE INVENTION
Some of the more popular digital image compression techniques used in
communication and data storage devices include various standardized
compression coding methods. For example, such compression techniques
utilize coding methods developed by the Moving Pictures Expert Group
(MPEG) or the Joint Photographic Experts Group (JPEG) in which discrete
cosine transform (DCT) and Huffman coding are used. Furthermore, the
methods may also utilize vector quantization or subband coding.
A block diagram of a conventional compression coding device which uses an
MPEG or JPEG compression coding method is shown in FIG. 1. As illustrated
in the figure, the device comprises a compression system for compressing
digital data and a decompression system for decompressing digital data. In
particular, the compression system comprises an input buffer 50, a
transform unit 52, a quantizer 54, a Huffman coding unit 56, and a
transmitter/recorder 58. In addition, the decompression system contains a
receiver/reproducer 60, a Huffman decoding unit 62, an inverse quantizer
64, an inverse transform unit 66, and an output buffer 68.
In order to compress a digital input image, the image is input to the
transform unit 52 via the buffer 50 and is transformed according to a DCT
function to produce various transform coefficients which correspond to the
image. Subsequently, the transform coefficients are output to and
quantized by the quantizer 54. Furthermore, the coefficients are not
quantized by subdividing them by a uniform interval, but are
differentially subdivided by a spatial frequency by using a human visual
system (HVS) 70. Then, the quantized coefficients are compressed by the
Huffman coding unit 56 in accordance with appropriate statistical
characteristics corresponding to the input image. Finally, the compressed
data is transmitted to a receiver or recorded on a recording medium by the
transmitter/recorder 58.
In addition, compressed data may be expanded into a restored image by the
decompression system. In particular, the components of the decompression
system perform functions which are similar but opposite to the functions
executed by the compression system.
In the DCT compression coding method shown in FIG. 1, an input image is
divided into many uniform blocks and a cosine function kernel is applied
to each block to enhance the compression by preventing the generation of
an overlapping image. However, even though a high compression rate may be
attained, a severe blocking effect is generated.
Also, the vector quantization method utilized by the compression system is
also advantageous due to its contribution to the high compression rate.
However, since such method requires excessive calculations for a codebook
training process and data compression, it cannot be used for real time
systems.
On the other hand, the subband method reduces the blocking effect which
occurs during high rates of data compression and is more efficient than
conventional DCT methods. However, such method cannot obtain a high
quality image since it employs a low compression rate.
Therefore, in order to overcome the above problems, a wavelet transform
(WT) method has been introduced. Since this method encodes image signals
based on time and frequency, the wavelet transform (WT) method is useful
for analyzing nonstationary signals and is advantageous because it is
similar to the human visual system (HVS).
Wavelet transformation (WT) is an integrated theory comprising a
multiresolution analysis of subband coding and a conventional method in
which images are divided into a plurality of subimages that are expressed
as a pyramidal structure. In other words, each subimage has hierarchical
information ranging from a lowfrequency band to a highfrequency band
such that more appropriate coding can be performed.
SUMMARY OF THE INVENTION
Accordingly, it is an object of the present invention to provide an
efficient image compression method using a wavelet transform technique.
It is another object of the present invention to provide a quantization
method in which quantization errors are minimized in an image compression
method using a wavelet transform technique.
It is still another object of the present invention to provide a method of
generating an effective tree list of transform coefficients in an image
compression method using a wavelet transform method.
It is yet another object of the present invention to provide a method for
coding the tree list.
It is still yet another object of the present invention to provide a method
for coding transform coefficients in an image compression method using a
wavelet transform technique.
In order to achieve one of the objects above, an image compression method
using a wavelet transform technique is provide. In particular, the method
comprises the steps of: (a) obtaining transform coefficients by
transforming an input image in accordance with the wavelet transforming
technique; (b) determining a quantizing interval which minimizes
quantization errors in a predetermined step size, wherein the quantization
interval is determined according to statistical characteristics of the
input image; (c) generating a simple tree structure based on the transform
coefficients; (d) modifying the simple tree structure by using statistical
characteristics of the transform coefficients to produce a monotonically
decreasing tree structure, wherein the monotonically decreasing tree
structure comprises a parent node and child nodes which correspond to the
parent node; (e) modifying the monotonically decreasing tree structure by
limiting a maximum height difference between the parent node and the child
nodes to produce a modified tree list; (f) quantizing the transform
coefficients based on the quantizing interval to produce quantized
transform coefficients; and (g) arithmetically coding the modified tree
list and the quantized transform coefficients.
In order to achieve another one of the objects above, a quantization method
is provided. Specifically, the method comprises the steps of: (a)
obtaining a density function p(x) based on a histogram of transform
coefficients; (b) manipulating the density function p(x) such that the
density function p(x) approximates a piece wise linear function; and (c)
determining the quantizing interval having minimal quantization errors
based on the piece wise liner function.
In order to accomplish still another object of the present invention, a
method of generating a tree list of wavelet transform coefficients is
provided. In particular, the method comprises the steps of: (a)
determining a height h(C.sub.ij) of the transform coefficients C.sub.ij ;
(b) modifying the transform coefficients C.sub.ij so that they
monotonically decrease; (c) generating the tree list based on the modified
transform coefficients C.sub.ij.
In order to accomplish yet another object of the present invention, a
method for coding a tree list is provide. Specifically, the method
comprises the steps of: (a) separating a set S of symbols in a modified
tree list into N subsets S.sub.1 to S.sub.N, wherein the symbols relate to
an input image and wherein the subsets S.sub.1 to S.sub.N are capable of
being independently coded and decoded; (b) determining a particular subset
S.sub.i of the subsets S.sub.1 to S.sub.N to which particular symbols of
the symbols belong based on previously coded information contained within
the modified tree list; (c) coding the particular symbols which correspond
to the particular subset S.sub.i by an arithmetic coder which corresponds
to the particular subset S.sub.i ; and (d) arithmetically coding at least
one quantized transform coefficient by dividing the quantized transform
coefficient into code data and size data and arithmetically coding the
code data and the size data.
BRIEF DESCRIPTION OF THE DRAWINGS
The above objects and advantages of the present invention will become more
apparent by describing in detail a preferred embodiment thereof with
reference to the attached drawings in which:
FIG. 1 is a block diagram showing a conventional image compression device;
FIG. 2A is a block diagram showing an embodiment of a coding device using a
compression coding method according to the present invention;
FIG. 2B is a block diagram showing an embodiment of a decoding device using
a decompression decoding method according to the present invention;
FIG. 3 shows a quantizing interval and a central value;
FIG. 4 shows a probability density function approximated as a linear
function;
FIG. 5 is a view of a tree structure of transform coefficients;
FIG. 6 is a graph comparing performances between a JPEG compression method
and a compression coding method according to the present invention; and
FIG. 7 is another graph comparing performances between the JPEG compression
and the compression coding method according to the present invention.
DETAILED DESCRIPTION OF THE INVENTION
FIG. 2A is a block diagram showing an image compression coder according to
the present invention. As shown in the figure, the device comprises a
wavelet transformer 10, a tree processor 12, a first arithmetic coder 14,
a quantizing interval determiner 16, a quantizer 18, a second arithmetic
coder 20, and a third arithmetic coder 22.
The wavelet transformer 10 inputs a digital input image and
wavelettransforms the image to generate corresponding transform
coefficients, and the tree processor 12 manipulates the transform
coefficients according to geometrical or statistical characteristics of
the image to produce a tree list. The first arithmetic coder 14 encodes
the tree list and transmits the encoded tree list to a receiver or records
the encoded tree list on a recording medium.
The quantizing interval determiner 16 inputs quantizer step size data from
an external source and inputs the transform coefficients output from the
wavelet transformer 10. Then, the determiner 16 calculates an appropriate
quantizing interval for quantizing the transform coefficients based on the
quantizer step size data. Afterwards, the quantizer 18 inputs the
transform coefficients from the transformer 10, the quantizing interval
calculated by the determiner 16, and the tree list output from the
processor 12. Then, the quantizer 18 quantizes the transform, coefficients
in accordance with the tree list and the quantizing interval and generates
code data and size data representing the quantized coefficients. The
second and third arithmetic coders 20 and 22 respectively input and
arithmetically encode the code and size data, and the encoded code and
size data are transmitted to the receiver or recorded on the recording
medium.
As shown in FIG. 2A, the tree processor 12 comprises a simple tree
processor 12a, a monotonic decreasing tree processor 12b, a difference
limit tree processor 12c, and a tree list formulator 12d. The simple tree
processor 12a inputs the transform coefficients from the wavelet
transformer 10 and generates a simple tree structure based on such
coefficients. In other words, the tree structure contains parent nodes and
child nodes which have values that are determined by the transform
coefficients.
The monotonic decreasing tree processor 12b inputs the simple tree
structure and determines if all of the child nodes have values which are
less than the value of the corresponding parent node. If the values of any
of the child nodes are larger than the value of the parent node, the
processor 12b changes the value of the parent node such that it is greater
than or equal to the value of child node. As a result, the processor 12b
inputs the simple tree structure and generates a monotonically decreasing
tree structure.
In addition to ensuring that the tree structure monotonically decreases,
the difference between the values of the parent node and each of the child
nodes should be smaller than a certain amount to increase the ability of
the device to predict the values of a child node based on the value of the
parent node. As a result, the monotonically decreasing tree structure is
input to the difference limit tree processor 12c to limit the magnitudes
of the differences between parent nodes and corresponding child nodes such
that the difference is less than a maximum value. After the difference
between the parent nodes and the child nodes is limited, the tree
structure is input by the tree list formulator 12d which generates a
corresponding tree list and outputs such tree list to the first arithmetic
coder 14.
FIG. 2B illustrates an image decompression decoder which decompresses the
image output from compression coder shown in FIG. 2A. The decoder
comprises a first arithmetic decoder 30, a second arithmetic decoder 32, a
third arithmetic decoder 34, and a wavelet inverse transformer 36.
The first arithmetic decoder 30 inputs the encoded tree list from the first
arithmetic coder 14 and outputs a corresponding decoded tree list. In
addition, the second and third arithmetic decoders 32 and 34 input and
decode the encoded code and size data from the second and third arithmetic
coders 20 and 22, respectively. Then, the inverse transformer 36 inputs
the tree list, the code data, and the size data corresponding to the
transform coefficients and outputs a restored image based on such data.
In order to more fully understand the operations of the various components
of the coder and decoder described above, some mathematical equations
relating to their operations will be described below. First, as shown in
FIG. 3, when a real number x is quantized, a representative value x of the
quantizing interval and a quantization value y.sub.i represents the value
x for the i.sup.th quantizing interval [d.sub.i, d.sub.i+1 ] can be
expressed as follows:
x.apprxeq.x=y.sub.i (1)
where d.sub.i .ltoreq.x<d.sub.i+1 and [d.sub.i, d.sub.i+1 ] denotes the
quantizing interval. As a result, a quantization error Err(x) generated
from such quantization can be determined according to the following
equation:
Err(x)=xx=xy.sub.i (2)
Accordingly, the mean square of the errors E can be computed as follows:
##EQU1##
where p(x) equals a probability density function. Furthermore, the
quantization value y.sub.i which minimizes the value of the mean square of
the errors E can be obtained by differentiating equation (2) and setting
its value equal to zero as follows:
##EQU2##
As shown in equation (4), the quantization value y.sub.i is an average of
the value x in the quantizing interval [d.sub.i, d.sub.i+1 ] when the mean
square of the errors E is minimized.
In the quantization method proposed in the present invention, uniform
quantization may performed based on a quantizer step size G, and the
quantizing interval [d.sub.i, d.sub.i+1 ] may expressed as [kGr,
(k+1)Gr]. In this instance, the input x is expressed as an integer
multiple k of the quantizer step size G, and the transform coefficient x
can be expressed as:
x.apprxeq.x=kG (5)
where kGr.ltoreq.x<(k+1)Gr for k.epsilon.Z, kG represents the
quantization value, and r represents a constant determined by the
quantizer step size G and by the statistical characteristics of the input
image. Thus, in order to minimize the mean square of the errors E of the
value kG, the value kG must be set to a value which satisfies the equation
(4). In other words, the most ideal quantizing interval [kGr, (k+1)Gr]
for selecting the value kG can be determined by the combining equations
(3) to (5) to produce the following equation:
##EQU3##
In order to determine a constant r which satisfies equations (3) through
(6), two methods may be used. In the first method, a histogram of the
wavelet transform coefficients of the input image is obtained, and a
probability density function p(x) which most closely represents the
histogram is determined by a KolmogorovSmirniv (KS) test or a x.sup.2
test. In the other method, the function p(x) is represented by a piece
wise linear function which approximates a histogram of the transform
coefficients.
Of the above methods, the latter method is more advantageous than the
former method. Specifically, in the former method, a substantial number of
various probability density functions p(x) are measured in order to
determine the appropriate function p(x) in accordance with the KS test or
the x.sup.2 test. Thus, many extensive and time consuming calculations
must be performed. Furthermore, if the probability density function p(x)
is incorrectly predicted, the accuracy of the quantization operation is
significantly degraded, and therefore, the KS test or the x.sup.2 test
cannot be practically used in a situation in which predicting statistical
characteristics (such as image signals) is difficult. Accordingly, in the
present invention, the constant r is determined by determining a piece
wise linear function which approximates the histogram.
FIG. 4 illustrates the method of linearly approximating the function p(x)
in order to determine the value of the constant r which most appropriately
corresponds to the input image signal. In this example, the function p(x)
may be approximated as the linear function p(x)=ax+b, in which a and b are
arbitrary constants. Accordingly, the approximated function p(x) may be
incorporated into equation (6) to produce the following equations:
##EQU4##
Then, the following quadratic equation can be obtained from equation (8):
ar.sup.2 [aG+p(kG)]r+aG.sup.2 /3+Gp(kG)/2=0
A quantization interval [kGr, (k+1) Gr] for a representative value kG is
set using the positive value of the two values of r satisfying equation
(9).
As mentioned above, the present invention employs a tree coding method for
effectively expressing the transform coefficients of the input image. Such
method obtains transform coefficients by wavelettransforming an input
image and expresses the coefficients as a tree structure. As a result, the
capability of efficiently using various systematic characteristics of the
wavelet transform coefficients is increased. An example of how the
wavelettransformed image information may be expressed as a tree structure
is shown in FIG. 5.
Specifically, if the transform coefficients are expressed according to a
corresponding quantizer step size G, the number of digits required to
express each transform coefficient is considered to be the "height" of the
transform coefficient, and the heights of various transform coefficients
are expressed as a tree structure. Accordingly, when a tree list is
recorded or transmitted, the values of the parent nodes and current nodes
of the tree structure correspond to the transform coefficients, and the
tree list contains information relating to the height between the parent
nodes and corresponding current nodes.
Also, the information represented by the heights denote the number of
information classes required to restore the corresponding transform
coefficients. As a result, a decoder is capable of restoring the transform
coefficients by reading the necessary height information.
1) Simple Tree Structure
As illustrated above, the simple expression tree processor 12a inputs
transform coefficients from the wavelet transformer 10. Based on the
coefficients, the processor 12a generates a simple tree structure having
parent nodes and child nodes and containing information relating to the
heights between the parent nodes and corresponding child nodes. The height
value h(C.sub.ij) of each transform coefficient C.sub.ij may be determined
according to the following equation when .vertline.C.sub.ij
.vertline..gtoreq.Gr:
##EQU5##
Furthermore, the height value h(C.sub.ij) equals zero when
.vertline.C.sub.ij .vertline.<Gr and .Ebackward.m.epsilon.Dc.sub.ij for
.vertline.m.vertline..gtoreq.G, and the height value h(C.sub.ij) equals
NULL when .vertline.C.sub.ij .vertline.<Gr and
.Ainverted.m.epsilon.Dc.sub.ij for .vertline.m.vertline.<G. In other
words, the height value h(C.sub.ij) is only determined by equation (10)
when the absolute value of the transform coefficient C.sub.ij is greater
than or equal to the difference between the quantizer step size G and the
constant r. In other words, the height value h(C.sub.ij) is determined by
equation (10) when .vertline.C.sub.ij .vertline..gtoreq.Gr. On the other
hand, when the difference between the quantizer step size G and the
constant r is greater than the absolute value of the transform coefficient
C.sub.ij (i.e. .vertline.C.sub.ij .vertline.<Gr), the height value
h(C.sub.ij) is not determined in accordance with equation (10).
Specifically, each of transform coefficients C.sub.ij may have one or more
child nodes Dc.sub.ij. If .vertline.C.sub.ij .vertline.<Gr and if the
absolute value m of at least one of the child nodes Dc.sub.ij is greater
than or equal to the quantizer step size G (i.e. if there exists a value
m.epsilon.Dc.sub.ij for .vertline.m.vertline..gtoreq.G), then the height
value h(C.sub.ij) is set equal to zero. On the other hand, if
.vertline.C.sub.ij .vertline.<Gr and if the absolute value of the value m
of every one of the child nodes Dc.sub.ij is less than the quantizer step
size G (i.e. if for every value m.epsilon.Dc.sub.ij,
.vertline.m.vertline.<G), the height value h(C.sub.ij) is set equal to
NULL.
The term "Dc.sub.ij " recited above represents the set of all child nodes
which correspond to the transform coefficient C.sub.ij. In addition, the
simple tree structure comprises tree information T(i,j) which corresponds
to the transform coefficient C.sub.ij. Moreover, the tree information
T(i,j) may express each transform coefficients C.sub.ij as the height
h(C.sub.ij) of the coefficient C.sub.ij such that T(i,j)=h(C.sub.ij).
In addition, if all values of the transform coefficients C.sub.ij and the
corresponding child nodes Dc.sub.ij are smaller than the quantizer step
size G, the height h(C.sub.ij) is set to a NULL value, and the values of
the child nodes Dc.sub.ij are not transmitted or recorded by the device.
Also, if the value of current transform coefficient C.sub.ij is smaller
than the quantizer step size G (such that the value of quantized
coefficient becomes zero) and some of the values of the corresponding
child nodes Dc.sub.ij are larger than the quantizer step size G, then the
height h(C.sub.ij) is set to zero.
When the tree list is only represented by the simple tree structure such
that the information T(i,j)=h(C.sub.ij), the height h(C.sub.ij) of a
parent node C.sub.ij may be less than the height h(Dc.sub.ij) of a
corresponding child node Dc.sub.ij. As a result, the height differences
between a parent and child nodes may equal a negative number. However, in
order to more easily predict the tree information T(i,j) corresponding to
the child nodes Dc.sub.ij, the tree information T(i,j) of the simple tree
structure should preferably monotonically decrease as one travels from the
parent node C.sub.ij to the corresponding child nodes Dc.sub.ij. In other
words, the height difference (and the information T(i,j)) between parent
and child nodes should equal a positive number.
2) Monotonically Decreasing Tree Structure
Since the tree information T(i,j) between a parent node and a child node of
the simple tree structure may not monotonically decrease, the tree
structure generated by the simple expression tree method may not
adequately represent the final tree list. Accordingly, the simple tree
structure containing the transform coefficients C.sub.ij is transformed
into a monotonically decreasing tree structure in accordance with the
following equation:
##EQU6##
As illustrated by equation (11), the tree information T(i,j) of the simple
tree structure is modified such that all transform coefficients C.sub.ij
correspond to information T(i,j) which monotonically decreases from the
parent node to the child node. Furthermore, each value T(i,j) of the
monotonically decreasing tree structure which equals zero is removed from
the remaining T(i,j) values.
However, even if the simple tree structure is transformed into a
monotonically decreasing tree structure, predicting the tree information
T(i,j) for at least some of the child nodes may still be difficult or
impossible. Accordingly, in order to more effectively code a tree list, a
monotonically decreasing tree structure should still be transformed such
that the information T(i,j) of the child nodes is more easily predictable.
3) Limiting the Difference Values
One method of transforming the monotonically decreasing tree structure such
that the value T(i,j) of the child nodes is more predictable is to limit
the difference Diff(C.sub.ij) between the value T(i.sub.p,j.sub.p) of the
parent node and the value T(i,j) of the child node. In particular, in a
monotonically decreasing tree structure, the difference Diff(C.sub.ij)
between the value T(i.sub.p,j.sub.p) of the parent node and the value
T(i,j) of the child node may be expressed by the following equation:
Diff(C.sub.ij)=T(i.sub.p,j.sub.p)T(i,j) (12)
However, predicting the various difference values Diff(C.sub.ij) is
difficult because statistical characteristics relating to input images
vary with each input image. However, predicting the value of the
difference Diff(C.sub.ij) may made easier if the difference Diff(C.sub.ij)
is restricted to be less than or equal to a predetermined maximum
difference Maxdiff. In other words, equation (12) could be modified as
follows:
T(i,j)=T(i.sub.p,j.sub.p)Maxdiff if T(i.sub.p,j.sub.p)T(i,j)>Maxdiff(13)
T(i,j)=T(i.sub.p,j.sub.p)Diff(C.sub.ij) if
T(i.sub.p,j.sub.p)T(i,j).ltoreq.Maxdiff
Accordingly, if the difference Diff(C.sub.ij) is restricted to be less than
or equal to the maximum difference Maxdiff, predicting the difference
Diff(C.sub.ij) is easier because it falls within a narrower range of
values. Therefore, if the difference Diff(C.sub.ij) is limited to Maxdiff,
the information T(i,j) of the child nodes is easier to estimate because it
falls within a range of values which are closer to the value
T(i.sub.p,j.sub.p) of the parent node.
4) Tree List Formulation
As indicated above, each node within the generated tree list generally has
a certain number of corresponding child nodes. However, if the values
T(i,j) value of a particular node is NULL, all coefficient values
Dc.sub.ij of the corresponding child nodes are less than or equal to the
quantizer step size G. As a result, the tree information T(i,j) of the
particular node is set to NULL and recorded on the tree list, and none of
the values T(i,j) of the corresponding child nodes are recorded.
For example, as illustrated in FIG. 5, a node contained within the lowest
band of the image (i.e. a node representing the lowest frequency
component) has only three child nodes. Furthermore, all nodes except for
the nodes of the highest band have four child nodes. Also, the nodes of
the highest band (i.e. the nodes representing the highest frequency
component) cannot have child nodes and cannot have values T(i,j) which
equal zero. Furthermore, the node of the lowest band cannot have a parent
node and is considered the root of each tree structure.
Based on the configuration above, the values T(i,j) of the parent and child
nodes are stored within the tree list during its creation. In particular,
the values T(i,j) of the child nodes are added to the tree list after the
value T(i,j) of the corresponding parent node is recorded in the tree
list.
5) Tree List Coding
After the tree list has been formed in the manner above, the tree list is
compressed according to an appropriate coding method. Two of the methods
by which the tree list may be compressed are the Huffman coding method and
the arithmetic coding method.
The Huffman coding method utilizes codes which have a minimum average code
length and is useful for instantaneous decoding. However, in order to use
such method, a predetermined probability value for each symbol used in the
entire tree list and an appropriate probability model must be known in
advance. Accordingly, a probability model appropriate for coding the tree
structure for various input images should preferably be determined since
the probability values for each symbol of the entire input image cannot be
obtained beforehand.
However, if the probability of the actual input image codes is different
from the probabilities contained in the predetermined probability model,
the compression efficiency of the Huffman coding method is significantly
reduced. Moreover, the compression efficiency is also substantially
lowered when a symbol has a large probability value (e.g. if the symbol
has a probability close to 1).
In light of the restrictions inherent in the Huffman coding method, the
present invention preferably employs the arithmetic coding method which
utilizes an adaptive model. In the arithmetic coding method, data
compression is performed by approximating the entropy of the tree list.
Moreover, since an adaptive model is used, providing a predetermined
probability model for the tree structure and a predetermined probability
value for each code within the tree structure are unnecessary.
In order to more easily understand the arithmetic coding method, some of
the mathematical equations and theories utilized by the method will be
described below. First, if an input image comprises a set S of M symbols
(i.e. S={x.sub.1,x.sub.2, . . . x.sub.M }) and if each symbol x.sub.j has
a probability density function p(x.sub.j) when the M symbols are coded,
the information volume I(x.sub.j) of the symbol x.sub.j and the entropy
H(S) of all of the coded M symbols are respectively represented by the
following equations:
##EQU7##
Furthermore, if the set S of M symbols is separated into N subsets S.sub.1
to S.sub.N which can be coded and decoded, the set S can be expressed as
the group of subsets S.sub.1 to S.sub.N as follows:
S=S.sub.1 .orgate.S.sub.2 . . . .orgate.S.sub.N ={x.sub.1,1, . . . ,
x.sub.1,p }.orgate.{x.sub.2,p+1, . . . , x.sub.2,q } . . .
.orgate.{x.sub.N,r+1, . . . , x.sub.N,M } (16)
If each subset S.sub.i (i=1 to N) is independently coded, the information
volume I(x.sub.ij) and entropy E.sub.i (S.sub.i) of each subset S.sub.i
can be expressed as follows:
##EQU8##
Furthermore, the probabilities p(x.sub.j) and p(x.sub.ij) (x.sub.ij
.epsilon.S.sub.i x.sub.j) can be used to compare the compression
efficiency of the data of the set S by using arithmetic codes.
Furthermore, if the set S is divided into N subsets S.sub.i, the
probabilities p(x.sub.j) and p(x.sub.ij) can be expressed as follows:
##EQU9##
Accordingly, when the set S is divided into N subsets S.sub.i and an
arbitrary symbol x.sub.j of an input image is coded, the entropy E(S) can
be determined based on the following equations:
##EQU10##
Furthermore, the relationship between the probabilities p(x.sub.ij) and
p(x.sub.j) relating to amount of information contained in identical
symbols x.sub.j and x.sub.ij (x.sub.ij .epsilon.S.sub.i x.sub.j) can be
expressed by the following equations:
##EQU11##
Moreover, since logarithms are monotonically increasing functions, the
following equations can be derived from equation (21b):
##EQU12##
As a result, the relationship between the entropy function E(S) (equation
(20)) and the entropy function H(S) (equation (15)) can be expressed as
follows:
E(S).ltoreq.H(S) (22)
p(x.sub.ij)I(x.sub.ij).ltoreq.p(x.sub.j)I(x.sub.j)
As demonstrated above, when a set S containing a group of M symbols is
given, an arbitrary symbol x.sub.j can be more effectively coded if the
subset S.sub.i containing the symbol x.sub.j can be determined. In other
words, the symbol x.sub.j can be more effectively coded if the previous
state indicates which arithmetic coder can code the symbol x.sub.j.
Furthermore, as previously stated, the image transform coefficients are
expressed as a monotonically decreasing tree structure, and the maximum
height difference between a parent node and child node of the tree
structure is limited by a predetermined maximum difference Maxdiff.
Accordingly, since the difference in height between the parent node and
the current node is used to calculate the height of the current node, the
type of symbol used to code the current node can be predicted based on the
parent node when the tree list is being generated. Examples of various
codes of arithmetic symbols which depend upon the state of the parent node
are expressed in Table 1.
TABLE 1
______________________________________
PARENT NODE
T(.,.) SYMBOL SET
______________________________________
1 {NULL, 0}
2 {NULL, 0, 1}
3 {NULL, 0, 1, 2}
4 {NULL, 0, 1, 2, 3}
5 {NULL, 0, 1, 2, 3, 4}
. .
. .
. .
T(.,.) > MAXDIFF {NULL, 0, 1, ...,
MAXDIFF}
______________________________________
As illustrated in Table 1, the tree list can be coded by separate
arithmetic coders which respectively encode symbols that correspond to the
various states of the parent node T(i,j). Consequently, the number of
arithmetic coders required for compressing the tree structure is equal to
the predetermined maximum difference Maxdiff+1.
6) Transform coefficient expression
The number of bits used to express each transform coefficient C.sub.ij in
accordance with the quantizer step size G can be determined from the
completed tree list. However, although both sign and magnitude bits are
generally required to express a number, the number can be expressed by the
following equation if the number of bits is already known:
##EQU13##
When expressing an arbitrary number "x" to be used in equation (23) where S
equals the height value of the transform coefficients of the parent node
of the child node having the tree information T(i,j) and the height value
h(C.sub.ij), the sign of "x" may be located in the most significant bit of
the data representing the number "x", and thus, the sign can be determined
by h(x). On the other hand, a decoder which decodes the value of
b.sub.h(x) is not required to know the value of the most significant bit
because the value of the most significant bit of b.sub.h(x) is always
equal to "1". As a result, the most significant bit position can be saved
when the magnitudes of all transform coefficients are stored in the tree
list.
In addition, the data that a coding device generally provides to a decoding
device is not the height value h(C.sub.im) relating to the transform
coefficient C.sub.ij but is the tree information T(i,j) relating to such
coefficient C.sub.ij. Consequently, the T(i,j) value is typically less
than or equal to the value of the height h(C.sub.ij). Therefore, if the
tree information T(i,j) is greater than the value of the height
h(C.sub.ij), a dummy sign is placed before the real value of the
coefficient which is expressed as the quantizer step size G. (See equation
(23)). Accordingly, in order to express one transform coefficient, the
code and size data are required, and such data are independently
compressed via the arithmetic coding method.
In accordance with one embodiment of the present invention, an Antonni 97
biorthogonal wavelet filter may be used as the wavelet filter.
Furthermore, the analysis level may be set to "6", and the predetermined
maximum difference value Maxdiff may equal "4". In addition, in order to
realize a border condition of a filter, a method of symmetric extension
may be used.
Also, in the image compression coding method of the present invention,
various compression ratios can be obtained depending on the value of
quantizer step size G. For example, such ratios may be obtained by using a
method which is similar to JPEG methods for obtaining various kinds of
compression ratios by changing the "quality factor".
In order to compare the performance of the image coding method of the
present invention with other coding methods, a 512.times.512 "Lena" image
(FIG. 6) and "Baboon" image (FIG. 7) with 256 gradations having different
statistical characteristics were compressed by a coder and decompressed by
a decoder in accordance with each method. Then, the restored image was
compared with the original image before compression (including the header
of the image) to determine the accuracy of each coder and decoder.
Also, the various compression coding methods were standardized with respect
to each other by using the same or similar arithmetic signs, models for
the arithmetic signs, a fixed model, and uniform probability. Furthermore,
compression was performed on data comprising a 14byte header in which
four bytes represented the size of the image, one byte represented the
level of the image, one byte represented the height of the transform
coefficient, and eight bytes corresponded to the quantizer step size G.
In addition, the probability density function for ascertaining the
quantizing interval was determined based on the histogram of the transform
coefficient (which was approximated as a linear function within the
quantizing interval). As a result, an efficient quantizing interval was
determined according to the value of the quantizer step size G.
FIGS. 6 and 7 respectively show the results of the "Lena" and "Baboon"
images after they have been decompressed by a decoder. Specifically, each
of the figures illustrate the change in picture quality (PSNR) of each
image as a function of the compression ratio (bpp). Also, in each of the
graphs, the results of the present invention are represented by solid
lines, and the results of the JPEG compression are represented by dotted
lines. Furthermore, in the comparative analysis, the JPEG compression
method employed a common image compression coding method such as DCT
coding.
Table 2 also illustrates a comparison among the coding method of the
present invention, the Shapiro coding method, and the Said coding method.
Since the Shapiro and Said coding methods employ a successive
approximation technique, each aspect of the coding methods could not be
directly compared with the coding method of the present invention.
However, all of the methods were compared while operating under the same
conditions to the furthest extent possible. In any event, the comparative
analysis was performed by compressing the Lena image by predetermined
compression ratios bpp in accordance with each method. Subsequently, the
image was decompressed based on each method, and the resultant change in
picture quality PSNR was observed. (In Table 2, the letter "G" denotes the
value of quantizer step size).
TABLE 2
______________________________________
ALGORITHM
RATE SHAPIRO SAID PRESENT INVENTION
______________________________________
0.25bpp (32:1)
31.33dB 33.69dB 33.83dB
(G:0.5139)
0.5bpp (16:1)
36.26dB 36.84dB 36.95dB
(G:0.2568)
1.0bpp (8:1)
39.55dB 40.12dB 40.21dB
(G:0.1261)
______________________________________
In the image compression coding method of the present invention, the height
of wavelet transform coefficient is expressed as a tree structure, the
tree structure is efficiently coded by arithmeticcoding, and an ideal
quantizing interval is determined based on a predetermined quantizer step
size. Consequently, image data can be compressed much more efficiently,
and the quality of the resultant restored image is substantially improved.
Furthermore, the method is capable of compressing data at a
highcompression rate to achieve lowPSNR and at a lowcompression rate to
achieve highPSNR.
Furthermore, the present invention may also be used in various other
applications besides image compression. For example, the invention may be
used for sound compression and can be utilized in image recording
equipment such as highdefinition televisions, filmless cameras, digital
videocassette recorders and camcorders, CD audio equipment, and
broadcasting equipment.
Furthermore, it is to be understood that the above described embodiments of
the invention are only illustrative and that modifications thereof may
occur to those skilled in the art. Accordingly, the present invention is
not to be regarded as limited to the embodiments disclosed herein, but is
to be limited only as defined by the appended claims.
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